Effects of Sample Size on Estimates of Population Growth Rates Calculated with Matrix Models

BACKGROUND: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of lambda. METHODOLOGY/PRINCIPAL FINDINGS: Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. CONCLUSIONS/SIGNIFICANCE: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities

Experimental Evaluation of Seed Limitation in Alpine Snowbed Plants

Background: The distribution and abundance of plants is controlled by the availability of seeds and of sites suitable for establishment. The relative importance of these two constraints is still contentious and possibly varies among species and ecosystems. In alpine landscapes, the role of seed limitation has traditionally been neglected, and the role of abiotic gradients emphasized. Methodology/Principal Findings: We evaluated the importance of seed limitation for the incidence of four alpine snowbed species (Achillea atrata L., Achillea clusiana Tausch, Arabis caerulea L., Gnaphalium hoppeanum W. D. J. Koch) in local plant communities by comparing seedling emergence, seedling, juvenile and adult survival, juvenile and adult growth, flowering frequency as well as population growth rates lambda of experimental plants transplanted into snowbed patches which were either occupied or unoccupied by the focal species. In addition, we accounted for possible effects of competition or facilitation on these rates by including a measure of neighbourhood biomass into the analysis. We found that only A. caerulea had significantly lower seedling and adult survival as well as a lower population growth rate in unoccupied sites whereas the vital rates of the other three species did not differ among occupied and unoccupied sites. By contrast, all species were sensitive to competitive effects of the surrounding vegetation in terms of at least one of the studied rates. Conclusions/Significance: We conclude that seed and site limitation jointly determine the species composition of these snowbed plant communities and that constraining site factors include both abiotic conditions and biotic interactions. The traditional focus on abiotic gradients for explaining alpine plant distribution hence appears lopsided. The influence of seed limitation on the current distribution of these plants casts doubt on their ability to readily track shifting habitats under climate change unless seed production is considerably enhanced under a warmer climate

Disease Dynamics in a Specialized Parasite of Ant Societies

Coevolution between ant colonies and their rare specialized parasites are intriguing, because lethal infections of workers may correspond to tolerable chronic diseases of colonies, but the parasite adaptations that allow stable coexistence with ants are virtually unknown. We explore the trade-offs experienced by Ophiocordyceps parasites manipulating ants into dying in nearby graveyards. We used field data from Brazil and Thailand to parameterize and fit a model for the growth rate of graveyards. We show that parasite pressure is much lower than the abundance of ant cadavers suggests and that hyperparasites often castrate Ophiocordyceps. However, once fruiting bodies become sexually mature they appear robust. Such parasite life-history traits are consistent with iteroparity– a reproductive strategy rarely considered in fungi. We discuss how tropical habitats with high biodiversity of hyperparasites and high spore mortality has likely been crucial for the evolution and maintenance of iteroparity in parasites with low dispersal potential

Accurate Inference of Subtle Population Structure (and Other Genetic Discontinuities) Using Principal Coordinates

Accurate inference of genetic discontinuities between populations is an essential component of intraspecific biodiversity and evolution studies, as well as associative genetics. The most widely-used methods to infer population structure are model-based, Bayesian MCMC procedures that minimize Hardy-Weinberg and linkage disequilibrium within subpopulations. These methods are useful, but suffer from large computational requirements and a dependence on modeling assumptions that may not be met in real data sets. Here we describe the development of a new approach, PCO-MC, which couples principal coordinate analysis to a clustering procedure for the inference of population structure from multilocus genotype data.PCO-MC uses data from all principal coordinate axes simultaneously to calculate a multidimensional "density landscape", from which the number of subpopulations, and the membership within subpopulations, is determined using a valley-seeking algorithm. Using extensive simulations, we show that this approach outperforms a Bayesian MCMC procedure when many loci (e.g. 100) are sampled, but that the Bayesian procedure is marginally superior with few loci (e.g. 10). When presented with sufficient data, PCO-MC accurately delineated subpopulations with population F(st) values as low as 0.03 (G'(st)>0.2), whereas the limit of resolution of the Bayesian approach was F(st) = 0.05 (G'(st)>0.35).We draw a distinction between population structure inference for describing biodiversity as opposed to Type I error control in associative genetics. We suggest that discrete assignments, like those produced by PCO-MC, are appropriate for circumscribing units of biodiversity whereas expression of population structure as a continuous variable is more useful for case-control correction in structured association studies